Line ratios from saved moment images

In this notebook, I will work with only pre-calculated line maps, which have already been extracted from the cube and have been corrected for the sky problems (at least in theory). The extraction process is carried out in the 03 series of notebooks.

Calculate reddening from Balmer decrement

Look at the raw Hα/Hβ ratio:

So we see a lot of structure there. In priniciple, lighter means more extinction. This seems to be real at the bottom of the image, where we see clear signs of the foreground filament.

But in other parts, the ratio is suspiciously well correlated with the brightness. So we need to fix that.

PyNeb calculation of intrinsic Balmer decrement

Calculate the theoretical Balmer decrement from PyNeb. Density and temperature from Valerdi:2019a

Look at correlation between Hα and Hβ in the faint limit

To make thinks easier, I multiply the Hb values by R0 so we have a square plot. I zoom in on the faint parts:

So, the slope is not unity, meaning the extinction is not zero. But the intercept is not zero either. Clearly, we must fix that

Correct zero point of Hβ map

That looks way better. Expand out to brighter pixels:

Final corrected Hα/Hβ ratio image

Now fix the Hb image and try again:

That is on the same brightness map as before, and it now completely eliminates the spurious structure associate with surface brightness – hurray!

Now define some regions to take averages

Plot on a better scale and show the regions:

We can see some very high extinction at in the S filaments. And some small increase in extinction in the main diagonal filament. This is probably limited having foreground emission to some extent.

Look at average values in the sample boxes

I tried mean and median, and it made very little difference. Lowest in the bow shock region; slightly higher in the west and central filaments. Much higher in the southwest filament.

The reddening law

PyNeb does not seem to have anything specifically tailored to the SMC. The average SMC extinction law is supposedly simply $1/\lambda$.

But, it is possible to get a SMC curve by using the "F99-like" option, which uses the curve of Fitzpatrick & Massa 1990, ApJS, 72, 163. This depends on $R_V$ and 6 other parameters (!!!). Most of the parameters only affect the UV part of the curve, which does not concern us.

Then, we can use the average values of $R_V$ and the other parameters, which were fit by Gordon:2003l to SMC stars. This is $R_V = 2.74 \pm 0.13$.

So here I compare that SMC curve with $1/\lambda$ and with the Clayton curve for Milky Way (but also adjusted to $R_V = 2.74$):

So the Gordon curve is flatter in the blue, steeper in green, and flatter in red, as compared to $1/\lambda$.

Test it out for the bow shock region:

And for the highest extinction region

So $E(B - V)$ varies from about 0.1 to about 0.35. This is similar to what is found for the stars.

The reddening map

We can now make a map of $E(B - V)$

Looks like I would expect. Check values in the boxes:

These seem the same as before. But we want to eliminate extreme values.

Save it to a file:

Lots of regions are affected by the stellar absorption. There are apparent increases in reddening at the position of each star. This is not real, but is due to the photospheric absorption having more of an effect on Hb (mainly because the emission line is weaker).

At some point, I am going to have to deal with that. But it is not an issue for the bow shock emission, since this is in an area free of stars. We should just use the median bow shock reddening of $E(B-V) = 0.087$ so that we don't introduce any extra noise.

Calculate the [S III] temperature

The raw ratio:

Oh dear, that is completely dominated by the zero-point error. But we can fix it!

So it is obvious that we need to add about 100 to the 6312 brightness. But we can already see that the slope of the relation gets shallower for 9069 > 1000 – so fainter is hotter!

Now we need to correct for reddening.

Now, make a mask of EW(6312). But first, we need to correct the zero point of the continuum.

Convert to actual temperatures with pyneb

The rather disappointing conclusion of this is that the [S III] temperatures do vary from about 13 to 16 kK, but they don't show anything special at the bow shock, being about 13.7 +/- 0.4 kK there.

Average over whole FOV is 14.2 +/- 0.8 kK after smoothing to eliminate the noise contribution. This implies $t^2 = 0.003$ in plane of sky, which is small.

Calculate [O III]/[S III]

Correct for extinction:

Quick look:

Fix zero points:

Calculate [O III] / Hβ

This might be better since at least it is not affected by reddening.

Calculate He I / Hβ

Let us see if this has a hole in it where the He II is coming from.

So 5875 is 10 to 100 times brighter than the other two. And it is almost identical to Hβ!

So if we correct it for reddening, then lots of spurious structure disappears. But we are left with very little variation at all, except for at the mYSO and the top right corner, which both show low He I.

Calculate He II / Hβ

So there is a tiny change in 5875/4861 from 0.109 to 0.107 as 4686/4861 increases.

Ratio of [Ar IV] / [Ar III]

Now we must subtract the He I line!

There is a slight temperature dependence, but almost no density dependence if we use the 5876 line. This is probably the best because it has good signal to noise.

We can assume that the He I temperature is the same as the [S III] temperature.

But we will check the other lines as well.

The 4922 has the same T-dependence as 5876, just 10 times weaker. The 5048 has a constant ratio, but it is so weak that we cannot use it. So 5876 it is ...

Average values of T and reddening to use in the corrections

We would introduce too much noise by using the pixel-by-pixel values of $T$ and $E(B - V)$, so we will construct an average value by using the He I brightenss as a weight, but masking out the mYSO

That looks OK. Now calculate some averages:

The avHe_Tsiii looks good. But to be honest, I am a bit suspicious of the avHe_EBV reddening, since there are lots of anomalous spots of high $E(B-V)$ that correspond to stars (presumably underlying stellar absorption affecting the Balmer decrement).

I could use the median instead, but I have ended up using the weighted one after all, since we seem to be oversubtracting if anything.

Take advantage to save extinction-corrected maps of the high-ionization lines. These are using the avHe reddening, not the pixel-by-pixel values

Now do the correction by faking the 4713 line and subtracting it:

Make a common minimal mask to use for all the [Ar IV] lines, which we will then combine with a brightness-based mask for the weaker lines and ratios:

I need to decide how bright a star needs to be before I mask out that bit of the image. 5000 in the cont4686 image seems a reasonable value.

That is looking good. Apply the mask to all the other images

Now find average reddening for [Ar IV] lines. Try two methods: (1) brightness-weighted mean; (2) make a mask based on the Ar IV brightness and then take median in that area.

So there isn't much difference. But we take the median since it should be less sensitive to those spots of higher $E(B-V)$ due to stars.

Apply extinction correction to all lines:

And replace the summed image:

Save the combined image, corrected for extinction:

So the density-sensitive ratio is $R_1 = 1.35 \pm 0.1$

So we are close to the low density limit, with a nominal value of 160. We need to get a very precise estimate of the uncertainty in order to get the error bars.

Now for the T diagnostics:

And do the one that is contaminated by C II

As expected, this last one is no good. But the others are fine. Now include density and temperature indiocators together:

Following function is copied from the matplotlib docs. Ideas originally from https://carstenschelp.github.io/2018/09/14/Plot_Confidence_Ellipse_001.html

I have modified it to include a weight array.